This subsection discusses the procedures that one can use to obtain approximate stress intensity solutions for complicated crack problems.  Approximate solutions should only be used when the objective of the damage tolerant analysis is to bound the answer and when due care has been taken to understand all aspects of the cracking behavior.  Most typically, the approximate solutions are derived using known (handbook) solutions that individually account for the effects of crack geometry, global geometry and loading.  As noted in subsection 11.2.1, stress-intensity factors can be added for different types of loadings when the global and crack geometries are the same.  This section will concentrate on those cases where the analyst must take existing solutions for several different geometries and estimate the stress-intensity factor for the geometry of interest.  In those cases where the individual geometric effects can be accounted for by multiplication of factors, the analysis is referred to as compound analysis.

There are three geometric factors that normally must be accounted for in an approximate damage tolerant analysis: stress concentration, finite width and crack shape.  The effects of all three factors on the stress-intensity factor can be established exactly using careful numerical analysis procedures.  However, the solution of damage tolerant problems requires more than the accurate development of the stress-intensity factor.  Frequently, the growth process causes the crack to constantly change its shape which significantly complicates the crack growth life analysis.

In order to describe how the three geometrical effects can be estimated, a series of examples are presented.  In each case, the approximate solutions are based on known solutions.  If the actual solution is available, it is compared to the approximate solutions.